Antigua has 365 beaches: one for every day of the year. But, as a father, your little darlings make it tricky to visit more than one of them. So that makes the task of choosing from each of the screensaver-grade paradises a little knotty, and that’s before you’ve worked out how you’re going to entertain the kids long enough to actually enjoy it.

But let’s rewind a bit. Why bother flying your baby 4,000 miles to this tiny Caribbean island in the first place? For an annual summer treat that’s exotic enough to set itself apart from the European mire, it’s a no-brainer. Direct flights, no vaccinations, no visas, more child-friendly hotels than neighbouring St Kitts and a far less package tour vibe than Barbados.

Then there’s Curtain Bluff. For a start, it’s set over two beaches, which doubles the amount of coastline you’re likely to actually visit. Secondly, it’s gently luxurious plantation-style suites overlook the coastline on the rising ground around the seaside, and are in striking distance of the bustle of Saint Johns and English Harbour. Thirdly, and most importantly, once you’ve paid, you’ve paid – this is as all-inclusive as you’ll get, with everything from the mini bar to the watersports rolled into the price.

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Which, as a new dad, is about as appealing as it gets in terms of intersecting your old life and new family. And when you get past the gates after an eight-hour flight it doesn’t let you down.

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The modest plantation-style buildings, sea views from every room and trad wicker furniture are every bit as Bond as you’d wish for (think Dr. No not Spectre) and there’s a pleasing lack of tech wizardry that tends to defines five-star resorts. Instead of a colossal TV, the furniture points towards wide sliding doors that open onto a beach view. Every other screen’s relegated to a little cinema room hidden upstairs above the main courtyard. As a compromise there’s strong WiFi throughout, so if yours has a robust Peppa Pig habit you’ll be able to get out of trouble.

Architecturally, it’s refreshingly simple, and a good acknowledgement that the drama of this place can’t compete with its own set. The bluff was bought in 1960 by hotel founder and ex-WWII pilot Howard Hoford, who spotted it while flying oil executives around the islands on charter planes for Texaco, but you don't need to be in the air to appreciate it. It's the kind of Caribbean loveliness beamed in from every pirate story you’ve ever read. Swaying palms, choppy ocean on one side, a calm bay on the other, and the guests-only beach means they can live their Jack Sparrow fantasies without either you or them worrying about who’s round the corner.

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When they get bored of that, which they will, you can cart them off to all sorts of activity groups. There’s accompanied Hobie Cat sailing, windsurfing, diving, water skiing, snorkelling boat trips, tennis coaching, basketball lessons, squash tuition, bocce and shuffleboard (also included in the price) - even the bounciest of your progeny will struggle to get through that lot in a week. In these kind of resorts, class sizes can get a bit… inner city, but because because it’s a relatively small resort (72 rooms in total), the activities aren’t overcrowded, so you won’t worry that your darling’s going to pick up too many bad habits.

That leaves you to sit down and put your feet up. And, for once, actually enjoy the place you’ve taken your children to. Which you will. The food’s superb – especially the lunches served on the beachside restaurant – the booze is free. There are lots of enticing relaxation offerings from the spa but, frankly, with the warm sea, respectfully unpopulated beaches and rum punch in whatever quantity you desire, you won’t need it. No wonder this place has a 65 per cent return rate.